arXiv research

A new method clusters subjects based on brain networks without vectorizing fMRI data.

Study optimal trading strategies with differing views and market prices.

We derive asset pricing formula for markets with incomplete information and subjective views.

A new method decomposes subjective risk into epistemic and aleatoric uncertainties.

New method extracts joint and individual signals from multi-view data.

Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern of learning machine. In [2,4], we discussed subjective spatial pattern, and estab…

Multi-view data, that is matched sets of measurements on the same subjects, have become increasingly common with advances in multi-omics technology. Often, it is of interest to find associations between the views that are related to the intrinsic class memberships. Existing association methods cannot directly incorpora…

New method considers subjectivity in text analysis using 'Room Theory'.

An outsider's overview of Anosov flows in 3D.

Proposes CI-GMVC to improve graph-based multi-view clustering performance.

Finding the most effective way to aggregate multi-subject fMRI data is a long-standing and challenging problem. It is of increasing interest in contemporary fMRI studies of human cognition due to the scarcity of data per subject and the variability of brain anatomy and functional response across subjects. Recent work o…

We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjec…

Correlated component analysis as proposed by Dmochowski et al. (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption that the involved spatial networks are identical. Here we propose a hierarchical pr…

Deep neural nets decode brain tasks from MEG data.

Almost para-quaternionic structures on smooth manifolds of dimension $2n$ are equivalent to almost Grassmannian structures of type $(2,n)$. We remind the equivalence and exhibit some interrelations between subjects that were previously studied independently from the para-quaternionic and the Grassmannian point of view.…

This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1. Combinatorial Complexes 2. Topological Invariants 3. Coverings 4. Galois Theory 5. G…

Multi-view data are increasingly prevalent in practice. It is often relevant to analyze the relationships between pairs of views by multi-view component analysis techniques such as Canonical Correlation Analysis (CCA). However, data may easily exhibit nonlinear relations, which CCA cannot reveal. We aim to investigate …

In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $ξ$ in a risk-conservative way relative to a family of probability measures $\mathcal{P}$. We first describe the evolutio…

Novel approach to learning models based on subjective timescales for better exploration and decision-making.

Bayesian Black-Litterman model updated to use market data for latent variables.

Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information …

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to inco…

We consider Thompson's groups from the perspective of mapping class groups of surfaces of infinite type. This point of view leads us to the braided Thompson groups, which are extensions of Thompson's groups by infinite (spherical) braid groups. We will outline the main features of these groups and some applications to …

The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus a…

The aim of this paper is to review and discuss in detail local aspects of principal bundles with groupoid structure. Many results, in particular from the second and third section, are already known to some extents, but, due to the lack of a ``unified'' point of view on the subject, I decided nonetheless to (re)define a…

Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of view. The subject has attracted scholars from across various disciplines, includin…

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le-Murakami-Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category of Jacobi diagrams. We prov…

Minimal surfaces with planar curvature lines are classical geometric objects, having been studied since the late 19th century. In this paper, we revisit the subject from a different point of view. After calculating their metric functions using an analytical method, we recover the Weierstrass data, and give clean parame…

Optimal order execution strategies for brokers under reference benchmarks.

MoReL models multi-omics data to find hidden molecular interactions.

CREIMBO models diverse brain activity by identifying hidden neural sub-circuits and their non-stationary interactions.

Study flat GL(1|1) connections using fatgraphs and coordinates.

The purpose of this book is to give an exposition of geometry, from a point of view which complements Klein's Erlangen program. The emphasis is on extending the classical Euclidean geometry to the finite case, but it goes beyond that. After a brief introduction, which gives the main theme, I present the main results, a…

We study the intrinsic geometry of area minimizing (and also of almost minimizing) hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. For any such hypersurface we define and construct a so-called S-structure which reveals some unexpected geometric and analytic properties of the …

Euler's elastica with monotone curvature is uniquely minimal.

Reinforcement Learning AI commonly uses reward/penalty signals that are objective and explicit in an environment -- e.g. game score, completion time, etc. -- in order to learn the optimal strategy for task performance. However, Human-AI interaction for such AI agents should include additional reinforcement that is impl…

Measurement error in observational datasets can lead to systematic bias in inferences based on these datasets. As studies based on observational data are increasingly used to inform decisions with real-world impact, it is critical that we develop a robust set of techniques for analyzing and adjusting for these biases. …

In this article we shall give an account of certain developments in knot theory which followed upon the discovery of the Jones polynomial in 1984. The focus of our account will be recent glimmerings of understanding of the topological meaning of the new invariants. A second theme will be the central role that braid the…

Contact reductions explained through symplectic reductions.

This is a survey paper on the topic of Weil-Petersson geometry of Teichmuller spaces. Even though historically the subject has been developed as a branch of complex analysis, the treatment here is from the view-point of differential geometry, much influenced by the works of Eells, Earle, Fischer, Tromba and Wolpert ove…

Deep learning models are growing, posing new mathematical challenges.

Analysing coronary artery plaque segments with respect to their functional significance and therefore their influence to patient management in a non-invasive setup is an important subject of current research. In this work we compare and improve three deep learning algorithms for this task: A 3D recurrent convolutional …

A new method detects hallucinations in medical image restoration using Fourier Ring Correlation.

We propose a novel method for multiple clustering that assumes a co-clustering structure (partitions in both rows and columns of the data matrix) in each view. The new method is applicable to high-dimensional data. It is based on a nonparametric Bayesian approach in which the number of views and the number of feature-/…

Let $C$ and $D$ be a pair of crumpled $n$-cubes and $h$ a homeomorphism of $\text{Bd }C$ to $\text{Bd }D$ for which there exists a map $f_h: C\to D$ such that $f_h|\text{Bd }C =h$ and $f_{h}^{-1}(\text{Bd }D)=\text{Bd }C$. In our view the presence of such a triple $(C,D,h)$ suggests that $C$ is "at least as wild as" $D…

Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real six-dimensional manifolds, can admit G-structures rendering them suitable for internal manifolds in supersymmetric flux compactifications. We develop techniques which allow us to systematically construct G-structures on SCTV and read off thei…

Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces called strata that are related to the moduli space of Riemann surfaces. There is a …

Bayesian method improves sparse CCA for multi-view data.